# Recitation 22

For equivalence relation, just remember the definition: an equivalent relation is a symmetric, reflexive and transitive relation.

Today, I also talked about ‘casting out nines’. It provides an effective way of probabilistic calculation verification.

For instance, if one wants to check whether $961\times 2414=2329854$ is correct. For the left hand side, $961\equiv 9+6+1\equiv 7 \mod 9$ and $2414\equiv 2+4+1+4=2\mod 9$, hence $961\times 2414\equiv 7\times 2=5\mod 9$. However, $2329854\equiv 2+3+2+9+8+5+4\equiv 6\mod 9$. So the calculation is incorrect.